Abstract
Partial differential equation is the center of mathematics and one of the important
pillars of other disciplines. Therefore, the research and exploration of the solution of
partial differential equation has always been an important direction for scientists to
discuss and explore, and to this end, great efforts have been devoted. In this paper, the
method of separating variables is one of the effective means to solve partial
differential equations.
Combined with the applicable conditions and application requirements of the
method of separation of variables, after comprehensive analysis of whether the partial
differential equation is homogeneous, the boundary conditions are homogeneous, the
boundary shape is regular, the partial differential equation is solved by the method of
separation of variables, and the process of solving the partial differential equation is
described comprehensively, and the partial differential equation under different
coordinate systems is also discussed. The equation was solved.
Partial differential equations are solved in this paper from the perspective of the
separation of variables method. Because the use of partial differential equations
covers all aspects of various fields, with the continuous development of various
disciplines, there are still many follow-up studies on this subject.
Key Words ： variable separation method;partial differential
equation;homo-
geneous;non homogeneous
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